Question

At NTP, the volume of a gas is found to be 273 ml. What will be the volume of this gas at 600 mm Hg and 273 $^\circ C$ ?
A.391.8 ml
B.380 ml
C.644 ml
D.750 ml

Answer 1

NTP stands for Normal condition of Temperature and pressure. This is considered to the ideal constant value while understanding the nature of the external parameters in a particular experimental setting. The values of temperature and pressure at NTP are given to be 293 K and 1 atm respectively.This question can be solved using a combined gas equation.

Complete step by step answer:
Now, let us write down the data that has been given to us:
Let the initial and final recorded temperatures be ${T_1}$ and ${T_2}$ respectively. Similarly let the initial and final recorded pressures and volumes of the given gas be ${P_1}$ , ${P_2}$ and ${V_1}$ , ${V_2}$ respectively.
To tabulate this data:
${T_1}$ = 293 K
${T_2} = {273^\circ }C$ $= \left( {273 + 273} \right)K = 546{\text{ }}K$
${P_1}$ = 1 atm = 760 mm of Hg
${P_2}$ = 600 mm of Hg
${V_1}$ = 273 ml
${V_2}$ = ‘x’ ml = ?
To solve this question, we are going to use a formula named the combined gas equation. This equation helps in establishing a relationship between the values of temperature, pressure and volume of a given gas at two different readings. The mathematical representation of this equation can be given by:
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
Rearranging the above equation:
${V_2} = \dfrac{{{P_1}{V_1}}}{{{T_1}}}.\dfrac{{{T_2}}}{{{P_2}}}$
Substituting the values form the given data in the above equation:
x = $\dfrac{{760x273}}{{293}}.\dfrac{{546}}{{600}}$
x = 644 ml
hence, the volume of the gas has been found to be 644 ml.

Hence, Option C is the correct option.

Note:

The combined gas equation is obtained from three different equations. It utilises the relations established in Boyle’s Law, Charles’ Law and Gay-Lussac law. Since it combines all these three relations, it is known as the Combined Gas equation.